Let's simplify the expression step by step:
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First, rewrite the expression: \[ 2 \cdot 2^2 + 8 \div 2 - (5 + 3) \]
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Calculate \(2^2\): \[ 2^2 = 4 \]
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Substitute \(2^2\) back into the expression: \[ 2 \cdot 4 + 8 \div 2 - (5 + 3) \]
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Perform the multiplication: \[ 2 \cdot 4 = 8 \]
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Now, substitute that back into the expression: \[ 8 + 8 \div 2 - (5 + 3) \]
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Next, calculate \(8 \div 2\): \[ 8 \div 2 = 4 \]
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Substitute that value back into the expression: \[ 8 + 4 - (5 + 3) \]
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Calculate \(5 + 3\): \[ 5 + 3 = 8 \]
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Substitute that back into the expression: \[ 8 + 4 - 8 \]
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Now, perform the addition and subtraction: \[ 8 + 4 = 12 \] and then \[ 12 - 8 = 4 \]
So, the final answer is: \[ \boxed{4} \]